The Supreme Court threw out a giant class-action suit against Walmart yesterday in a long-awaited decision that was seen as a boost for big business.

Smacking down the biggest worker-discrimination case in history, the justices ruled unanimously that a sex-bias suit that sought to unite 1.5 million of Walmart’s female employees couldn’t proceed as a class action against the discount chain.

The plaintiffs — who had been seeking billions of dollars in back pay, charging that Walmart held back raises and promotions for female employees — failed to prove that the alleged woes were the result of a single corporate policy, the court ruled.

While Walmart officially prohibits discrimination, plaintiffs led by Walmart greeter Betty Dukes had argued the Arkansas-based retailer had a “culture of bias,” and that local managers were given leeway as they passed over women while doling out pay raises and promotions.

To bolster their case, the plaintiffs cited statistics — now a decade old — that found women accounted for 70 percent of Walmart’s hourly workers but just 33 percent of its managers.

Justice Antonin Scalia, writing for the conservative majority that sided with Walmart, said the plaintiffs were still “worlds away” from proving institutional bias. He noted that a sociologist brought by plaintiffs as an expert witness had declined to estimate what percentage of promotions and pay raises had been infected with bias.

The judges were unanimous in ruling that the class-action suit couldn’t advance in its current form because of procedural issues, reversing a decision by the Ninth Circuit Court of Appeals.

But the court was split 5-4 along ideological lines as it essentially blocked the case from getting another chance — a decision that experts said may deal a blow to class-action suits against big companies in the future.

Writing for the dissenting minority, Justice Ruth Bader Ginsburg said she would have allowed plaintiffs to sue under another provision of class-action rules.

The justice said there was evidence that “gender bias suffused Wal- Mart’s corporate culture” and that “senior management often refer to female associates as ‘little Janie Qs.’ “